This Week: Math Significant Figures or Digits Chem Atoms and Periodic Table

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This Week(Math) Significant Figures (or Digits)
(Chem) Atoms and Periodic Table!
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First Lets Review Last Week

• Numbers vs. Units
• Measured Numbers vs. Counted numbers
• Scientific Notation
• Conversions in the Metric System
• Lab Safety (with video!)
• The Basics of a Lab Report

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Uncertainty in Measurement

• Significant Figures
• Indicates the exactness of measurements
• Significant is not the same as important
• 1 and .001 have the name number of significant
  figures. Clearly the zeros in .001 are important,
  but they are not significant. Significance
  refers to the exactness of the measurement.

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Uncertainty in Measurement

• What is the difference between 7g and 7.00g?
• Which measurement would have the most sig. figs?
  
• 1000 miles
• 1.56 miles
• .000045 miles
• Answer 1.56 miles with 3 sig. figs

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Significant Figure Guidelines

• Flashcard Alert!
• 1. Nonzero digits are always significant.
• 2. Zeros trapped between nonzero numbers are
  always significant. (2002 has 4 significant
  figures)
• 3. Zeros at the beginning of a numberare never
  significant they just showthe position of the
  decimal point. (.005 has only 1 significant
  figure)

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Significant Figure Guidelines

• 4.Zeros that fall at the end of a number after a
  decimal point are always significant. (.00500 has
  3 sig figs)
• 5.Numbers at the end of a number are only
  significant if the follow a decimal point! To be
  sure, convert to scientific notation.
• -700 has 1 significant figure -7.00 x 102 has
  3 significant figures

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Stop and Practice!
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Significant Figures in Calculations

• Multiplication and Division
• Base your answer on the number with the fewest
  significant figures!
• Round your final answer if it has more than the
  allowed number of significant figures.

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Example of Multiplication

• If you multiply 1.23 and 4.567, you get 5.61741.
• 1.23 has three significant figures,
• 4.567 has four.
• Solution? Round your answer to three significant
  figures! Write the answer as 5.62.

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Significant Figures in Calculations

• Addition and Subtraction
• Base your answer on the number with the fewest
  significant figures to the right of the decimal
  point.
• Round your final answer if it has more than the
  allowed number of significant figures.

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Example of Addition

• If you add 1.23 and 4.567, you get an answer of
  5.797. But 1.23 and 4.567 have different number
  sig figs after the decimal. Here you are
  limited to two sig figs after the decimal point.
  Round your answer like this! 1.23 4.5675.797 so
  ?5.80

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Rounding Off Significant Figures

• When the answer to a calculation contains too
  many significant figures, it must be rounded off.
  There are 10 digits that can occur in the last
  decimal place in a calculation (0,1,2,3,49).
• If the digit is smaller than 5, drop it and leave
  the remaining number unchanged. Example 1.684
  becomes 1.68.
• If the digit is 5 or larger, drop it but add 1 to
  the previous digit. Example 1.247 becomes 1.25.